Spin and statistics of quantum kinks

Apart from some brief and inconclusive remarks concerning the problem of spin and statistics of quantum kinks in space-time dimension D>2, a detailed discussion of the D=2 situation is given. The main result is that two-dimensional quantum kinks are statistical 'schizons'; they exist in the same Hilbert space either as bosons or as fermions. In those cases where one can introduce local kink-sector generating operators as in the sine-Gordon model, the Bose and Fermi fields are strictly local fields, which are relatively non-local with respect to each other. (Auth.)